Perimeter of Right Angle
2026-02-21 21:11 Diff
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Last updated on December 28, 2025

The perimeter of a shape is the total length of its boundary. For a right-angled triangle, the perimeter is the sum of the lengths of its three sides. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a right-angle triangle.

What is the Perimeter of a Right Angle?

The perimeter of a right-angle triangle is the total length of its three sides. By adding the length of the two legs and the hypotenuse, we get the perimeter of the shape.

The formula for the perimeter of a right-angle triangle is\( ( P = a + b + c ),\) where  a  and b  are the legs, and c is the hypotenuse.

For instance, if a right-angle triangle has sides,  a = 3 ,  b = 4 , and  c = 5 , then its perimeter is P = 3 + 4 + 5 = 12 .

Formula for Perimeter of Right Angle - P = a + b + c .

Let’s consider another example of a right-angle triangle with side lengths,  a = 5 ,  b = 12 , and  c = 13 . So the perimeter of the right-angle triangle will be:  P = a + b + c = 5 + 12 + 13 = 30 .

How to Calculate the Perimeter of Right Angle

To find the perimeter of a right-angle triangle, we just need to apply the given formula and sum all the sides of the triangle.

For instance, a given right-angle triangle has the sides of  a = 8 ,  b = 15 ,  c = 17

Perimeter = sum of all sides = 8 + 15 + 17 = 40  cm.

Example

Problem on Perimeter of Right Angle -

For finding the perimeter of a right-angle triangle, we use the formula,  P = a + b + c .

For example, let’s say,  a = 9  cm,  b = 12  cm, and  c = 15  cm.

Now, the perimeter = sum of all sides =  9 + 12 + 15 = 36  cm

Therefore, the perimeter of the right-angle triangle is 36 cm.

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Tips and Tricks for Perimeter of Right Angle

Learning some tips and tricks makes it easier for children to calculate the perimeter of right-angle triangles. Here are some tips and tricks given below:

  • Always remember that a right-angle triangle's perimeter is simply the sum of the three sides of the shape. For that, use the formula,  P = a + b + c .
  • Calculating the perimeter of a right-angle triangle starts by determining the length of each side using the Pythagorean theorem if needed. For a right-angle triangle, the relation \(( a^2 + b^2 = c^2 )\) can be used to verify the hypotenuse.
  • To reduce the confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of right-angle triangles. After that, apply the formula to each triangle.
  • To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture.
  • If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations, like using the base and height, often use the semi-perimeter.

Common Mistakes and How to Avoid Them in Perimeter of Right Angle

Did you know that while working with the perimeter of a right-angle triangle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:

Problem 1

A right-angle triangle has a perimeter of 30 inches. Two of its sides are 9 inches each. To find the missing side, subtract the sum of the known sides from the total perimeter.

Okay, lets begin

Length of the missing side = 12 inches.

Explanation

Let ‘c’ be the side of the missing side. And the given perimeter = 30 inches. Length of the two equal sides = 9 inches.

Perimeter of right-angle triangle = sum of lengths of three sides. 30 = 9 + 9 + c

30 = 18 + c

c = 30 – 18 = 12

c = 12

Therefore, the missing side is 12 inches.

Well explained 👍

Problem 2

A wire with a perimeter of 60 inches is reshaped into a right-angle triangle. The two legs are equal in length. Find the length of each leg if the hypotenuse is 24 inches.

Okay, lets begin

18 inches

Explanation

Given that the perimeter of the wire is equal to the total length of the wire and this wire is reshaped into a right-angle triangle, here is the solution: Perimeter of the right-angle triangle = Total length of the wire

Let each leg be 'a'. Perimeter = a + a + 24

60 = 2a + 24

60 - 24 = 2a

36 = 2a a = 18

Therefore, the length of each leg of the triangle is 18 inches.

Well explained 👍

Problem 3

Find the perimeter of a right-angle triangle whose legs are 7 cm and 24 cm.

Okay, lets begin

54 cm

Explanation

Using the Pythagorean theorem, the hypotenuse  c  is calculated as follows:  \((c = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 ) \)cm.

Perimeter of triangle = a + b + c

P = 7 + 24 + 25 = 54

Therefore, the perimeter of the triangle is 54 cm.

Well explained 👍

Problem 4

Ben is planning a right-angle triangular flower bed in his garden. He measures the two legs of the bed: Leg A = 5 meters Leg B = 12 meters How much fencing should Ben buy to go around the edge of the flower bed?

Okay, lets begin

Ben will need 36 meters of fencing to go around the garden.

Explanation

Using the Pythagorean theorem, the hypotenuse  c  is calculated as follows:

\( ( c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 ) \)meters.

The perimeter of the triangle is the sum of all the three sides. Using the formula: P = a + b + c

P = 5 + 12 + 13 = 30 meters.

Well explained 👍

Problem 5

Find the perimeter of a right-angle triangular path with legs 9 meters and 40 meters.

Okay, lets begin

Sides are a = 9, b = 40, c = 41

Perimeter = a + b + c = 9 + 40 + 41 = 90 meters.

Explanation

Using the Pythagorean theorem, the hypotenuse  c  is calculated as follows:

\( ( c = \sqrt{9^2 + 40^2} = \sqrt{81 + 1600} = \sqrt{1681} = 41 )\) meters.

The entire distance is calculated around the path to be 90 meters by summing the lengths of the three sides.

Well explained 👍

FAQs on Perimeter of Right Angle

1.Evaluate the right-angle triangle’s perimeter if its sides are 6 cm, 8 cm, and 10 cm.

Perimeter of triangle = a + b + c, Hence ( P = 6 + 8 + 10 = 24 ) cm.

2.What is meant by a right-angle triangle’s perimeter?

The total length around a right-angle triangle’s sides is its perimeter. In other words, the perimeter of a right-angle triangle is the total length of its sides.

3.What are the types of triangles?

There are six types of triangles: Equilateral triangle, Isosceles triangle, Scalene triangle, Acute triangle, Right triangle, and Obtuse triangle.

4.Which triangle has no equal sides?

A scalene triangle is a triangle with no equal sides. All three sides of the scalene triangle are different.

5.Which triangle has the smallest perimeter?

The orthic triangle has the smallest perimeter for a given set of altitudes.

Important Glossaries for Perimeter of Right Angle

  • Perimeter: The total length of the sides of a shape.
  • Right-angle Triangle: A triangle with one angle measuring 90 degrees.
  • Legs: The two sides of a right-angle triangle that form the right angle.
  • Hypotenuse: The longest side of a right-angle triangle, opposite the right angle.
  • Pythagorean Theorem: A mathematical formula\( ( a^2 + b^2 = c^2 ) \)used to calculate the hypotenuse of a right-angle triangle.

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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

Fun Fact

: She has songs for each table which helps her to remember the tables